In mathematics, a pointed set is a set with a distinguished element, which is called the basepoint. Maps of pointed sets (based maps) are those functions that map one basepoint to another, i.e. a map such that . This is usually denoted
- .
Pointed sets may be regarded as a rather simple algebraic structure. In the sense of universal algebra, they are structures with a single nullary operation which picks out the basepoint.
The class of all pointed sets together with the class of all based maps form a category.
A pointed set may be seen as a pointed space under the discrete topology or as a vector space over the field with one element.
Famous quotes containing the words pointed and/or set:
“Semantically, taste is rich and confusing, its etymology as odd and interesting as that of “style.” But while style—deriving from the stylus or pointed rod which Roman scribes used to make marks on wax tablets—suggests activity, taste is more passive.... Etymologically, the word we use derives from the Old French, meaning touch or feel, a sense that is preserved in the current Italian word for a keyboard, tastiera.”
—Stephen Bayley, British historian, art critic. “Taste: The Story of an Idea,” Taste: The Secret Meaning of Things, Random House (1991)
“Is it enough
That the dish of milk is set out at night,
That we think of him sometimes,
Sometimes and always, with mixed feelings?”
—John Ashbery (b. 1927)